THE YANG BAXTER EQUATION AND RELATED ALGEBRAIC STRUCTURE
The principal aim of the project is the construction and the study of set-theoretical solutions of the Yang-Baxter equation. Currently it is really incisive in this context the research of linkage between solutions and some algebraic structures, e.g., I-type monoids (Tate and Van den Bergh, 1996), braces (Rump, 2005), skew braces (Guarnieri e Vendramin, 2017).
Mainly, we will analyse the linkage between the solutions and the semi-braces, a recent structure introduced by Catino, Colazzo and Stefanelli (2017), by the study of algebraic aspects to construct new set-theoretical solutions of the Yang-Baxter equation.
Further, we will analyse the linkage between the solutions and the Hopf-Galois extensions that play a key role in the study of Quantum Groups and actually are object of many research works.
This job comes from a partnership with Science Magazine and